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Let us start here from Square one. No... from zero.
Back in my day, you had to come up with your own trolls instead of posting an image macro! You kids have it easy! Avatar/Sig courtesy of TheEroKing
Guild Wars 2 SN: ArchonWing.9480 MyAnimeList || Reviews

The Nichijou previews were all random stuff from the episode being voiced by a famous voice actor and had nothing to do with the next episode.

Norio Wakamoto as the wooden cube of power was awesome.
As was Aya Hirano as a King piece on a cake.

*brofist*

I do remember Angel Beats' preview shorts where they basically throw in a bunch of random, mixed up dialogue in one package. Oh the nostalgia. The preview for the third episode had a scream in the end saying "DON'T TOUCH IT!" IIRC

Legend of the Galactic Heroes, narrator always spoiling the next episode

That's one of the reasons I always skip previews when I marathon anime (it's also kinda boring and pointless since I can watch the next episode right away).

There are only a few series where I cared about watching the previews because they were actually funny and interesting, but that's basically what was already mentioned in this thread.

The ones from Cowboy Bebop, Nichijou and Haruhi are definitely something that you can't simply skip.

Clannad had also an interesting take on them, by taking and piecing dialogues from the next episode completely out of contest thus giving a completely wrong impression (it was clannad that did that right? I'm not sure, I've watched too many anime.)

In Abenobashi Mahou Shoutengai the main boy, Saatchi, wants to deliver the previews at the end of every episode, but events transpire that keep him from doing so. Usually his friend Arumi delivers the preview, or they squabble over who will play that role.

Texhnolyze... those blurry scenes, projected onto a weird, angular surface, and the episode title, illegible at first, then slowly coming into focus...
Also Paranoia Agent, as already mentioned.
Ergo Proxy had one too, similar to the one from Higurashi. Both increasing the already thick atmosphere.